Lasts Longer...

This is the sort of gem you come to KPC to see folks.  Data in the service of social science.  And that's why Mr. Overwater invented the internet.  (Data, I mean, not what follows here.  Mr. Overwater has standards, and I do not mean to besmirch him in any way...)

Overall, and as a general matter...the internet is for porn (NSFW, and juvenile, but still).

And since it is, that raises a question you didn't even know you didn't know the answer to (at least, I didn't know):  What is the average time spent ...um...enjoying a porn site?  An "interval of viewing," if you will?

Well, now you know.

Go, China! 

Humanprogress.org

Interesting initiative from CATO:

Humanprogress.org is a comprehensive database that aims at spreading rational optimism to people around the world. We cautiously collect data from many reliable sources, and show our findings in a new viewer-friendly webpage. Since it includes very comprehensive data on various research topics, it might be able to provide scholars with very useful and reliable evidence for their arguments.

The Tip of the Data Spear

Nod to Kevin Lewis

Unit--root-toot-tootin'

Friday (like most days), Brad DeLong said some amazing stuff.

In particular he claimed that, "There Are Two Unit Roots and Strong Mean Reversion in U.S. GDP per Capita".

Yikes.

Phone call for Clive Granger.

First off, unit roots and mean reversion are incompatible concepts. A unit root is essentially a stochastic trend. There is no fixed mean of the series to revert to.

Second, "two unit roots" means that real gdp per capita is I(2). Which means in English that shocks to the growth rate are permanent, that the variance of the growth rate continually increases over time, and that there is no mean reversion in the growth rate.

We actually have a lot of statistical tests for unit roots. Sure they are not so great, especially in the power department. So if we fail to reject the null, we are not thrilled about rolling with it.

But if we can reject the null, the size of the tests (probability of rejecting a true null) are not far from accurate, especially over longer time periods, and we have over 200 years of data to work with!


So here's the augmented Dickey-Fuller test for a unit root in the growth rate of real GDP per capita(the null is that there is such a unit root):


********************************************************************************

Null Hypothesis: D(LRYPC) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on Modified SIC, MAXLAG=14)

                                                                t-Statistic                     Prob.

Augmented Dickey-Fuller test statistic          -11.43155                  0.0000
Test critical values:  1% level                        -3.461630
                             5% level                        -2.875195
                           10% level                        -2.574125

*MacKinnon (1996) one-sided p-values.

 *********************************************************************************

We are rejecting (crushing) the null of a second unit root in the series at the 0.01 level. You can click through all the options in EVIEWS on lag length selection and get exactly the same rejection.

There are not two unit roots in real US GPD per capita.

Here's a graph of the growth rate of real GDP per capita in the US since 1800:

The data run from 1801 to 2010 (I'm pretty sure it's the same data Brad used).

The mean of the series is around 0.015, or a 1.5% growth rate. As you can see, while there is evidence of volatility clustering, the series is strongly mean reverting and shocks to the growth rate are decidedly not "highly persistent"  (i.e. it does not have a unit root).

There is even a big debate about whether real GDP per capita has even one unit root, because there are a lot of processes (long memory, Markov switching, structural breaks, breaking trends) that are not unit root processes but typical tests will fail to reject the null of a unit root anyway.